Within an hour of sending his first Hyperloop tweet, Musk followed up with a few more details. He tweeted, "Still a lot of work needed to receive formal approval, but am optimistic that will occur rapidly."

That last point about quickly building the Hyperloop is one civil engineers, developers and government leaders may scoff at due to the red tape that goes along with almost every infrastructure project.

Later in the afternoon, the Boring Company told CNBC that it "has had a number of promising conversations with local, state and federal government officials. With a few exceptions, feedback has been very positive and we have received verbal support from key government decision-makers for tunneling plans, including a Hyperloop route from New York to Washington, D.C."

The spokesman said the company expects to get the approvals it needs to break ground later this year.

"From a physical engineering standpoint it is a concept that I believe is doable," said Malcolm Dougherty of the California Department of Transportation. "But the complications get into where do you put it and what right-of-way rights do you have to be able to build it."

In other words, the devil is in the details. CNBC asked Musk's Boring Co. to clarify which government agency or agencies have told Musk they approve of his Hyperloop plan, but has not yet received a response.

At some point, papers will have to be filed, government agencies will likely hold public reviews and the long process of building one or more tunnels spanning more than 200 miles will begin.

Regardless of the location, the same critical question will confront Musk and his team: Do they plan to burrow under public or private property?

"If he is going to do it underground, you still have to acquire right of way and property rights to be able to go under there," Dougherty said. "There are a lot of things underground in Los Angeles like building foundations, sewer lines and utilities."

In the meantime, the mayoral offices of at least three cities that are expected to house Hyperloop stations said they have not been involved in any talks with Musk or The Boring Co.

Philadelphia city government spokesman Mike Dunn told CNBC in an email that Musk has had no contact with Philadelphia officials.

"We do not know what he means when he says he received 'government approval,'" Dunn said. "There are numerous hurdles for this unproven Hyperloop technology before it can become reality."

In similar fashion, the press secretary for New York City Mayor Bill DeBlasio tweeted that this was the first he had heard of the project and that he had no clue what "verbal approval" meant.

"This is the first we heard of it too, but we can't wait to hear more," said Susana Castillo, press secretary for Washington Mayor Muriel Bowser, in an email to CNBC.

The White House said it has talked to Musk, but gave no indication of when the talks took place or whether any kind of approval was granted.

"We have had promising conversations to date, are committed to transformative infrastructure projects, and believe our greatest solutions have often come from the ingenuity and drive of the private sector," said a statement from a White House spokesman.

Musk ended the afternoon by imploring people supportive of the idea to let their elected officials know.